The first term is the loss of inference model, which can be viewed as a regularizer, encouraging the model to learn disentangled feature by putting a prior over latent variable [1]}. The second term is the reconstruction loss of the generative model. Suppose \(x_{m,t} = \mathbf {f}_m(t) + \epsilon _{m,t} + \mathbf {e}_{m,t}\)  is an anomaly, and its associated reconstruction distribution is \(\hat{x}_{m,t}=\mathcal {N}(\mu _{m,t}, \sigma _{m,t})\) . The generative model tries to reconstruct the contaminated \(x_{m,t}\) , rather than the true signal \(\mathbf {f}_m(t)\) , otherwise the reconstruct loss, which is the negative log likelihood \(-p_{\theta _{}}(x_{m,t}|\hat{x}_{m,t})\)  will be high. To minimize the objective loss function from the data with anomalies, the model will either learn a biased mean \(\mu _{m,t}\) , or an over-estimated variance \(\sigma _{m,t}\) . As a result, the Sequential VAE can be vulnerable to anomalies.
